Neurologic complications secondary to cerebrovascular damage are prevalent in children with homozygous Sickle Cell Disease. These patients experience both clinically-overt cerebrovascular accidents and "silent infarctions," demonstrated by Magnetic Resonance Imaging (MRI). They are also at risk for neurocognitive abnormalities. We hypothesize that daily, low-dose, aspirin therapy will safely diminish the incidence and progression of cognitive deficits, as well as the pre-disposition to overt and silent stroke in children with homozygous Sickle Cell Disease. In order to optimize the design of a future trial to test this hypothesis, we propose a randomized, placebo-controlled, double-blind pilot study. The trial's primary objective is to evaluate the safety and tolerability of daily low-dose aspirin in children with Sickle Cell Disease. The secondary objectives are: 1. To establish the level of compliance with aspirin administration. 2. To identify the most useful assessments in a battery of age-appropriate neurocognitive tests. 3. To assess the feasibility of MRI and Magnetic Resonance Angiography (MRA) studies, and the utility of classification systems for use in group comparisons. 5. To establish trends in Transcranial Doppler (TCD) ultrasound velocities over time, and the validity of using trends in group comparisons. 6. To obtain preliminary data regarding the effect of aspirin on the incidence of cognitive deficit, imaging abnormalities, overt stroke, painful crises, and Acute Chest Syndrome. 7. To establish the feasibility of recruiting patients. A minimum of 60 patients will be enrolled. Subjects will include children between the ages of 3 and 10 years, with documented homozygous Sickle Cell Disease who are currently followed at the Galisano Children's Hospital (University of Rochester Medical Center, Rochester, New York), and at Saint Luke's-Roosevelt Hospital Center (Columbia University, New York, New York). Subjects will be randomized to one of two treatment groups, daily aspirin (1-2.5 mg./kg./day), or placebo. Patients will receive therapy for 18 months. There will be careful laboratory and clinical monitoring every 3 months, and more frequently as needed. Group comparisons regarding pre- and post-treatment clinical complications, neurocognitive testing, MRI, MRA, and TCD studies will be made.